History is written by the victors: this is a truism that has become a cliche. Yet over three hugely influential centuries of world history – from the sixth to the 4th century BC – accounts of the Mediterranean come solely from the the little Greek states that were mere gnats on the western flank of the giant bull of the Persian empire.

The story of the Mediterranean and Mesopotamian world (and beyond) should be that of the this empire, the largest by far that the world had yet known, matched across subsequent millennia only by Imperial Rome and Han China. Yet through accidents of culture, the Persians have merely walk-on parts for most students of history – on stage merely to play the nasty tyrants in the Ionian revolt, the sneaky baddies at Thermopylae and a clumsy Goliath at Salamis, as the Greek cheerleader, Herodotus, unfolds his tale.

Turn the historic lens through 180 degrees, however, and the world looks very different: “The petty squabbles, alliances and disputes of these states on the edge of the empire … were of little or no importance to either the Great Kings or the Persian Empire as a whole. The Persian ‘invasions’ of Greece in the fifth century BC were expeditions to punish specific instances of Greek interference in Asia Minor. Afterwards it was the skilful diplomacy of able satraps that maintained the stability of the Western frontier.”

Those words are from the newly opened Forgotten Empire: the World of Ancient Persia exhibition at the British Museum. The first major show on this world civilisation in London, perhaps in the West, to focus on the Persians, it aims to swing that lens, to present the conquerors in their own terms.

The show begins with a statue that amply illustrates the size and reach of the Persian empire at its height. Of Darius, who is now sadly lacking his head, it was found in Susa, although probably carved in Egypt, and around its edge the people of his empire are shown in 24 cartouche fortresses. They are Persian, Mede, Elamite, Arian, Parthian, Bactrian, Sogdian, Arachosian, Drangian, Sattogydian, Chorasmian, Sakan, Babylonian, Armenian, Lydian, Cappadocian, Skudrian, Assyrian, Arabian, Egyptian, Libyan, Nubian, Makan and (No, I’ve never heard of a third of those either.)

Next is a room lined with spectacular casts from Persepolis, the Persians’ great palace that was vandalously destroyed by Alexander. Made in 1892, they now preserve details lost in the originals. It’s an understandable decision – these large panels of processing figures are spectacular, but they have that curiously flatness of fascimile that is impossible to overcome. What really demands attention are smaller carvings, often only fragments, polished still, so many centuries after their creation, to a metallic gleam. The descendants of the wonderful Assyrian bulls next door, this is an art at its zenith – generations of craftsmen have studied the human and animal form until the bend of a bull’s knee, the curve of a man’s eyebrow, are perfectly understood.

Then it is on to eating and drinking, from spectacular gold and silver rhytons (drinking horns), to silver and glass dishes that would, we’re told, have held meals of tastes still recognisable Persian today – one dinner was of sweet grape jelly, candied turnips, capers and radishes with salt, and pistachio nuts.

The sweep of life is completed in the next room, where spectacular gold jewellery, most from funerary contexts, competes with stone carving for the claim of the ultimate Persian art. One gold earring – quite possibly to be worn by a man, the carvings suggest – is a fist-sized, astonishingly intricate, assemblage of dozens of rings and spirals, set inside each other like a Russian doll. Just looking at it made my earlobes ache.

So we’ve done ceremony and royalty, we’ve done everyday life, we’ve done death. Yet there’s something missing – the Persians themselves. There’s only a few of King of Kings and a handful of satraps. No children; no women; no labouring peasants. There’s no human stories – not even myths – and no Tutenkhamen-style tombs with all their pathetic human interest.

But this, it seems, is not the fault of the curators. The Persians themselves are to blame. They were great warriors, great administrators and great diplomats. But for their place in posterity, they relied on art and wealth. Their society didn’t cultivate a Herodotus; their kings failed to ensure their tombs would not be robbed soon after their deaths. They’ve left us wonderful things, but not wonderful stories. Unless those are rediscovered, the Persians, even with this effort on their behalf, are likely to remain shadowy boogeymen.